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Definition: Soundness and Completeness of a Logical Calculus
A logical calculus $L$ is called
 sound, if any derivable statement is also a valid statement, formally $\vdash \phi$ implies $\models \phi,$
 complete, if any valid statement is also derivable, formally $\models \phi$ implies $\vdash \phi.$
Notes:
 Soundness and completeness are semantical properties of a logical calculus.
 A logical calculus is sound if all its theorems are true statements, and it is complete if all true statements are theorems.
 Soundness and completeness are desirable properties of logical calculi since such systems induce no difference between the provability and the truth of theorems.
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References
Bibliography
 Hoffmann, Dirk W.: "Grenzen der Mathematik  Eine Reise durch die Kerngebiete der mathematischen Logik", Spektrum Akademischer Verlag, 2011
 Beierle, C.; KernIsberner, G.: "Methoden wissensbasierter Systeme", Vieweg, 2000